Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

What is the volume of a sphere with radius 5?

  1. 125\pi

  2. 250\pi

  3. 375\pi

  4. 500\pi
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a sphere with radius r is given by the formula (V = \frac{4}{3}\pi r^3). Substituting r = 5 into the formula, we get: (V = \frac{4}{3}\pi (5^3) = \frac{4}{3}\pi \cdot 125 = 375\pi). Therefore, the volume of the sphere is 375\pi.

Multiple choice

A cylinder is a three-dimensional geometric figure that has two circular bases and a curved surface. What is the volume of a cylinder with radius 4 and height 6?

  1. 96π

  2. 192π

  3. 288π

  4. 384π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder with radius r and height h is given by the formula πr^2h. Therefore, the volume of a cylinder with radius 4 and height 6 is π * 4^2 * 6 = 96π.

Multiple choice

What is the area of a circle with radius 7 cm?

  1. 49π cm^2

  2. 147π cm^2

  3. 196π cm^2

  4. 225π cm^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a circle is given by A = πr^2, where r is the radius. If the radius is 7 cm, then the area is 147π cm^2.

Multiple choice

A circle has an area of 36π square units. What is the length of its radius?

  1. 3 units

  2. 4 units

  3. 5 units

  4. 6 units
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of a circle is given by (A = πr^2), where r is the radius. If the area is 36π square units, then the radius is 6 units.

Multiple choice

What is the area of the sector of a circle with radius 12 cm and central angle 60 degrees?

  1. 18π cm^2

  2. 36π cm^2

  3. 54π cm^2

  4. 72π cm^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a sector of a circle is given by (A = \frac{θ}{360}πr^2), where θ is the central angle in degrees, r is the radius, and π is the constant pi. If the radius is 12 cm and the central angle is 60 degrees, then the area of the sector is 36π cm^2.

Multiple choice

What is the volume of a cylinder with radius 3 and height 5?

  1. 45π

  2. 90π

  3. 135π

  4. 180π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is given by the formula $V = πr^2h$. Substituting the given values, we get $V = π(3)^2(5) = 45π$.

Multiple choice

What is the area of a sector of a circle with radius 10 and central angle 60 degrees?

  1. 25π

  2. 50π

  3. 75π

  4. 100π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a sector of a circle is given by the formula $A = (θ/360)πr^2$, where θ is the central angle in degrees and r is the radius of the circle. Substituting the given values, we get $A = (60/360)π(10)^2 = (1/6)π(100) = 25π$.

Multiple choice

What is the volume of a sphere with radius 6?

  1. 36π

  2. 72π

  3. 108π

  4. 144π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by the formula $V = (4/3)πr^3$. Substituting the given value, we get $V = (4/3)π(6)^3 = 36π$.

Multiple choice

What is the area of a circle with radius 5 cm?

  1. 25π cm^2

  2. 50π cm^2

  3. 75π cm^2

  4. 100π cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is given by the formula πr^2. Therefore, the area of a circle with radius 5 cm is π(5)^2 = 25π cm^2.

Multiple choice

Find the volume of a cylinder with radius 4 cm and height 8 cm.

  1. 100π cm³

  2. 200π cm³

  3. 300π cm³

  4. 400π cm³
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. In this case, r = 4 cm and h = 8 cm, so V = π(4²)(8) = 300π cm³.

Multiple choice

Find the surface area of a cylinder with radius 5 cm and height 10 cm.

  1. 314 cm²

  2. 157 cm²

  3. 78.5 cm²

  4. 39.25 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cylinder is given by SA = 2πr(r + h), where r is the radius and h is the height. In this case, r = 5 cm and h = 10 cm, so SA = 2π(5)(5 + 10) = 314 cm².

Multiple choice

Find the volume of a cone with radius 3 cm and height 4 cm.

  1. 12π cm³

  2. 24π cm³

  3. 36π cm³

  4. 48π cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 3 cm and h = 4 cm, so V = ½π(3²)(4) = 12π cm³.

Multiple choice

Find the surface area of a cone with radius 6 cm and height 8 cm.

  1. 150.79 cm²

  2. 75.39 cm²

  3. 37.69 cm²

  4. 18.84 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cone is given by SA = πr(r + l), where r is the radius, l is the slant height, and h is the height. In this case, r = 6 cm and h = 8 cm. To find l, we use the Pythagorean theorem: l² = r² + h². Substituting the values, we get l² = 6² + 8² = 100. Therefore, l = 10 cm. Now we can calculate the surface area: SA = π(6)(6 + 10) = 150.79 cm².

Multiple choice

Find the volume of a sphere with radius 5 cm.

  1. 523.6 cm³

  2. 261.8 cm³

  3. 130.9 cm³

  4. 65.45 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by V = ½πr³, where r is the radius. In this case, r = 5 cm, so V = ½π(5³) = 523.6 cm³.